Codeforces Round 957 (Div. 3) |
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Finished |
One of the first programming problems by K1o0n looked like this: "Noobish_Monk has $$$n$$$ $$$(1 \le n \le 100)$$$ friends. Each of them gave him $$$a$$$ $$$(1 \le a \le 10000)$$$ apples for his birthday. Delighted with such a gift, Noobish_Monk returned $$$b$$$ $$$(1 \le b \le \min(10000, a \cdot n))$$$ apples to his friends. How many apples are left with Noobish_Monk?"
K1o0n wrote a solution, but accidentally considered the value of $$$n$$$ as a string, so the value of $$$n \cdot a - b$$$ was calculated differently. Specifically:
Learning about this, ErnKor became interested in how many pairs $$$(a, b)$$$ exist for a given $$$n$$$, satisfying the constraints of the problem, on which K1o0n's solution gives the correct answer.
"The solution gives the correct answer" means that it outputs a non-empty string, and this string, when converted to an integer, equals the correct answer, i.e., the value of $$$n \cdot a - b$$$.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.
For each test case, a single line of input contains an integer $$$n$$$ ($$$1 \le n \le 100$$$).
It is guaranteed that in all test cases, $$$n$$$ is distinct.
For each test case, output the answer in the following format:
In the first line, output the integer $$$x$$$ — the number of bad tests for the given $$$n$$$.
In the next $$$x$$$ lines, output two integers $$$a_i$$$ and $$$b_i$$$ — such integers that K1o0n's solution on the test "$$$n$$$ $$$a_i$$$ $$$b_i$$$" gives the correct answer.
32310
3 20 18 219 216 2218 2214 1 165 162 1 1262 2519
In the first example, $$$a = 20$$$, $$$b = 18$$$ are suitable, as "$$$\text{2}$$$" $$$\cdot 20 - 18 =$$$ "$$$\text{22222222222222222222}$$$"$$$- 18 = 22 = 2 \cdot 20 - 18$$$
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